Pluriadjoint bundles of polarized surfaces
type: Item
instance of: scholarly article
title: Pluriadjoint bundles of polarized surfaces
zbMATH Open document ID: 0714.14005
DOI: 10.1007/BF01298854
published in: Monatshefte für Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178458
review text: Let L be an ample line bundle on a complex projective smooth surface X. The spannedness and the very ampleness properties of the pluriadjoint bundles \((K_ X\otimes L)^{\otimes t}\), \(t\geq 2\), are investigated by using Reider's theorem [\textit{I. Reider}, Ann. Math., II. Ser. 127, No.2, 309-316 (1988; Zbl 0663.14010)]. If (X,L) is not in a special list and \((X',L')\) denotes the reduction of (X,L), then (1) \((K_{X'}\otimes L')^{\otimes 3}\) is very ample; (2) \((K_{X'}\otimes L')^{\otimes 2}\) is ample and spanned and is very ample unless X contains an irreducible curve satisfying some special conditions; (3) the map associated with \(\Gamma ((K_{X'}\otimes L')^{\otimes 2})\) has degree \(\leq 4\), equality implying that \(\chi\) (\({\mathcal O}_ X)=0\) and \(g(L)=2\).
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4175122
zbMATH Keywords: spannedness
zbMATH Keywords: very ampleness
zbMATH Keywords: pluriadjoint bundles
author: Antonio Lanteri
reviewed by: Antonio Lanteri
MaRDI profile type: Publication
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OpenAlex ID: W2093398525
description: scientific article; zbMATH DE number 4175122